22^' BE LINEIS CTRVIS QVAE 



fcribanuir arcns circularcs ME,?;;^, et diicantur chordae 

 BE, Af, cum radiis KE, Kt^, vocenturque OB,/; KA, a» 

 Atque erit pernaturamEpicycloidis MG:GCz=:2^-+-^; 

 b, et GC^^MG,=:^-^, BE, ob BE-MG , igitur 

 MC=:M€+GC==:BE-+-GC=:\^^ BE. Perhypothe- 

 fin cft MC : AwrzOB : OKz=:b: aa-^-b , ergo erit 

 A?//zi:^^MCzz^-^±^^BE. porro per naturam curuac 

 habetur Am : A^rr2^-4-2^: b^ vnde Amzi:''.^^ At. 

 Erit itaque ^--'^t'" BE-^-±ti^ A^, hoc eft, chordae BE 

 et Ae erunt acquales. 



«2. E centro circuli mobihs R ducatur in conta- 

 dam G re^fl-i RG , atque e ccntro F in contadum H re- 

 dix FH, quae produdlae concurrent in centro O. Etquo- 

 niam arcus circnlares funt in ratione compofita angulo- 

 ruiii etradiorum •, ent H;z: HB=:HF?2x^:HOBxZ', inde 

 ob, H^^rzHB deducitur HOB=:4 HF«. 



3. E(l itaque angulus ;;/NP— HOBH-OHNrr 

 HOB -f- /f/HF=-HOB -f- iHF« =r-JHF«-4-iHF/2=: 

 -.^^HFw. Quoniam autem chordae /;/H, ^B aequales 

 funt, ex natura Epicycloidis, erit quoqueH?/— A^~EB. 

 dem. n. i. et HFwrzEKB ; igitur ;//N/) i=:£±f ' HFwzz: 

 ^^EKB , atquc ob re(flum inp, angulus ;?;«N— 90- 

 f«N;)ir90-^^EKB. 



4 Pari modo angulus PMLrrMGR-MQGn: 

 EBK-MQG=rEBK-'//OGi=:EBK--DOG-r/OD ; fed 



ob 



